A Global Existence Result for the Quasistatic Frictional Contact Problem with Normal Compliance

We consider the quasistatic problem of the contact of an elastic body with a rigid foundation in the presence of friction. The contact condition is taken as a power law normal compliance. We prove, for forces and initial data that are not too large, the existence of a solution u such that u ∈ C([0, T]; H 1(Ω) and d u/dt ∈ L 2 (0, T; H 1 (Ω)). The main tools are from the theory of differential inclusions.

[1]  Solution of Signorini-like contact problems through interface models—I. preliminaries and formation of a variational equality , 1987 .

[2]  A. Klarbring,et al.  Duality applied to contact problems with friction , 1990 .

[3]  L. Andersson,et al.  A quasistatic frictional problem with normal compliance , 1991 .

[4]  Equations d'évolution dans un espace de Hilbert, associées à des opérateurs sous-différentiels , 1973 .

[5]  J. T. Oden,et al.  Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws , 1987 .

[6]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[7]  J. Oden,et al.  Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , 1987 .

[8]  Solution to Signorini-like contact problems through inter-face models—11. existence and uniqueness theorems , 1988 .

[9]  J. Simon.  Compact sets in the spaceLp(O,T; B) , 1986 .

[10]  A. Klarbring,et al.  FRICTIONAL CONTACT PROBLEMS WITH NORMAL COMPLIANCE , 1988 .

[11]  Meir Shillor,et al.  On friction problems with normal compliance , 1989 .

[12]  G. Micula,et al.  Existence and Uniqueness Theorems , 1992 .

[13]  P. Panagiotopoulos.  Inequality problems in mechanics and applications , 1985 .

[14]  The rigid punch problem with friction , 1991 .

[15]  J. T. Oden,et al.  Models and computational methods for dynamic friction phenomena , 1984 .

[16]  J. Oden,et al.  Existence and local uniqueness of solutions to contact problems in elasticity with nonlinear friction laws , 1986 .

[17]  F. P. Bowden,et al.  The Friction and Lubrication of Solids , 1964 .

[18]  C. M. Elliott,et al.  Constrained anisotropic elastic materials in unilateral contact with or without friction , 1991 .

[19]  Strong solutions for parabolic variational inequalities , 1978 .